Google tells me that is more of a system with preparatory schools in France. That said, there is more of an emphasis at some schools than others in individual interactions and seminars at the undergraduate collegiate level. I had some of that--just not mostly in engineering. In US elite schools, there's certainly time conflict for professors given research priorities.

Yes, this is part of the French prépa/CPGE system, which is the "standard" way for students to enter elite engineering schools. You do your first 2-3 years of undergrad in prépa.

Source: I did prépa.

This is a false friend translations - CPGE are undergraduate programs (that are prepatory to further studies at the graduate levels).

It happens to some degree in the US. I got a Masters at a school (after a BS at another school) that had 4-year BA degrees that you could extend to an additional 1-year BE degree.